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# Beam angle in folded telescope design ...

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With "simple" telescope designs - like newtonian and refractor, F/ratio of telescope calculated like focal length / aperture also describes light cone that such telescope produces.

When coming to a focus, light beam on principal axis will be "wide" some distance before focus to the same ratio as F/ratio of the scope (beam will have the same "shape" as F/ratio of the scope).

Does this hold true for folded design as well, given that primary is strongly curved and secondary magnifies that image?

Here is an example that confuses me:

I've got RC scope, it has 85mm central obstruction and it is safe to say that secondary mirror is not that big - it is baffled and also it's support is larger than mirror diameter (by at least 5-10mm). It is also safe to say that rays perpendicular to optical axis will not illuminate fully secondary mirror (otherwise - any rays that are at a slight angle will start vignetting straight away, and there is quite large illuminated field).

Telescope is physically long about 580mm with focuser and focus point is 159mm from 2" connection of focuser - which gives total of about 740mm from the front of the tube. Primary mirror is not placed directly at beginning of the tube, but rather some distance inside - let that be 3-4cm for collimation mechanism, and let the mirror it self be 1cm - so let's say total of 50mm. So we have about 690mm of separation between secondary mirror and focal plane.

If we take that about 75mm (85mm minus support / baffling and some distance to secondary edge) of secondary is casting rays to center of focal plane (from all rays parallel to optical axis) - and we divide that two numbers - 690 and 75, we get : F/9.2 rather than F/8.

I used arbitrary assumptions here, but I tried to stay "on the safe side". If we assume that all central obstruction is in fact illuminated secondary and it produces F/8 beam, then focal plane needs to be located at ~680mm from secondary mirror. Still possible, but I think that first scenario is more realistic and that light beam on back side of telescope is slower than F/ratio of scope would suggest because of magnifying secondary.

Another example would be TS 8" F/12 Cassegrain telescope. Tube is ~620mm long, back focus is 150mm, together that gives 770mm. Central obstruction is 33% linear - which would mean 67mm (203mm * 33%), and at F/12, 67mm secondary would need to focus at 804mm. That is further than tube+backfocus and not even considering that secondary is not located at tube beginning but a bit further in. Beam at the back side of scope clearly can't be F/12 and needs to be faster in this case.

Does anyone have any idea what is in fact happening in the case of folded telescope design?

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Tbe same basic geometric optics applies but you can't use the approximations commonly used in manual ray tracing. This is particularly true when one element compensates for the aberrations of the other.

Ray tracing programs are the way to go. However,  I am sure to first order,  simple geometric optics should get close to give the basic layout.

Not totally clear on your question but I would calculate the diameter of the beam the primary makes at the secondary using the spacing and the primary mirror diameter and focal length.  Then use this with the net F ratio to find output beam  dimensions.

Regards Andrew

PS or you can work back the other way if you don't have the main mirror details.

Edited by andrew s

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3 minutes ago, andrew s said:

Tbe same basic geometric optics applies but you can't use the approximations commonly used in manual ray tracing. This is particularly true when one element compensates for the aberrations of the other.

Ray tracing programs are the way to go. However,  I am sure to first order,  simple geometric optics should get close to give the basic layout.

Not totally clear on your question but I would calculate the diameter of the beam the primary makes at the secondary using the spacing and the primary mirror diameter and focal length.  Then use this with the net F ratio to find output beam  dimensions.

Regards Andrew

That is a very good point, I would need F/ratio of primary mirror and exact spacing between primary and secondary - to calculate illuminated diameter on secondary, and then secondary to focal plane distance to see the shape of the beam - that of course being approximation since secondary is not flat, but curved (but slightly, and it would not change things much). However, I don't have those for my scope (maybe 8" F/8 designs don't differ, and I'll be able to find info online). I wanted to do some calculations for SA200 and F/ratio of beam is important for coma and curvature (finally figured why and how) - and slower is better, but I wondered if beam is in fact slower than F/ratio of the scope would suggest.

Maybe easiest way to explain the question, given F/8 RC telescope, is marked ratio 8 as well:

(that ratio being almost the same as illuminated diameter on secondary - illumination coming from rays parallel to optical axis - and secondary to focal plane distance).

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Posts crossed see my PS

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13 minutes ago, andrew s said:

PS or you can work back the other way if you don't have the main mirror details.

Can you please be more specific - not sure what to do or even where to start.

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For SA200 calcs just use the output focal ratio znd main mirror diameter as this is what counts. With my ODK I just used F6.8  and 400mm diameter

What I mean is that you can start from the focal point and project back to the secondary mirror usi g the output focal ratio. The diameter there will be less than the secondary mirror diameter. Using this and the  main mirror diameter you can estimate the main mirrors F ratio and focal length. This assumes it is not oversized.

Regards Andrew

Edited by andrew s

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3 minutes ago, andrew s said:

For SA200 calcs just use the output focal ratio znd main mirror diameter as this is what counts. With my ODK I just used F6.8  and 400mm diameter

What I mean is that you can start from the focal point and project back to the secondary mirror usi g the output focal ratio. The diameter there will be less than the secondary mirror diameter. Using this and the  main mirror diameter you can estimate the main mirrors F ratio and focal length. This assumes it is not oversized.

Regards Andrew

But that is exactly my question. I know that F/ratio of my scope is F/8 because it is 200mm / 1600mm scope.

Does this mean that output focal ratio is going to be the same? It certainly is with refractor and newtonian telescope, but folded designs mean light changes angles (fast primary and magnifying secondary) - and I'm just not sure that output "focal ratio" will be the same as focal ratio of telescope calculated by focal length / aperture.

Output "focal ratio" is important to SA200 calcs because it produces coma in spectrum and spectrum field curvature.

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Yes it will F8. If you are seeing limited then it does not matter if it's a compound telescope or not apart from the light loss due to the obstruction.

In your SA200 calcs just use 200mm F8. If I remember correctly he main aberration is chromatic coma which along with the star size due to seeing limits the resolution in a slitless converging beam configuration.

Regards Andrew

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Just now, andrew s said:

Yes it will F8. If you are seeing limited then it does not matter if it's a compound telescope or not apart from the light loss due to the obstruction.

In your SA200 calcs just use 200mm F8. If I remember correctly he main aberration is chromatic coma which along with the star size due to seeing limits the resolution in a slitless converging beam configuration.

Regards Andrew

Actually main blur is due to field curvature at those parameters. Seeing limit can be "overridden" by grating distance - star profile stays the same in arc seconds and hence pixels, but dispersion can be increased so one can have less nm/pixel and hence less nm / star blur.

Due to diffraction formula:

Not all rays that would otherwise be focused at the same place (and are in 0 order image) will be bent by the same amount, that causes two issues - spectrum coma and focal point shift. It's a bit like in this image:

Central ray that is perpendicular gets bent by exact angle. "Left" ray gets bent slightly differently then "Right" ray. They no longer intersect in single point (coma) and they intersect a bit "before" regular focal plane. This point of intersection depends on wavelength so we have a curved line of places of best focus.

Only one point on the spectrum will be in perfect focus - and others will be slightly defocused (out focus on one side and in focus on the other). According to calculations, in my case that is the "worst" offender.

That can be compensated to a degree if multiple images of spectrum are obtained with focusing on different parts of spectrum instead on the middle and then composing spectrum out of multiple parts - around point of best focus.

Anyways, I was under impression that F/ratio of the scope can be different than F/ratio of exit beam in compound scopes, because I see focal length as measure of conversion of angle to linear distance in focal plane, and was not sure if shape of exit beam had anything to do with ratio of focal length and aperture, but it might be that those two are tied together and link is not obvious to me.

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Vlaid,

Check out the TransSpec spreadsheet - I think you have a copy.

It shows the effect of focus and chromatic aberrations.

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@vlaiv you can mitigate the spectral curvature by tilting the sensor with respect to the optic axis but then it makes the rest of the field defocused.

Also you need to keep the first order on the image to allow calibration of star without obvious sharp lines. This limits the grating chip distance you can have although vignetting  will also be an issue if you go too far.

Good luck with the project.

Regards Andrew

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Although we are now diverging from main topic - which was about angles of exit beam, I'll just comment on SA200 part.

In fact, in the light of a new day, I think that my original question for this thread was sort of silly. I'm don't quite understand it yet, but it sort of stands to reason that exit beam must be of exact shape as F/ratio of the scope even in folded design - because focal length is function of geometry (and aperture stays the same).

Back to SA200. @Merlin66, this all in fact started by me examining trans spec and wondering why one can't have more resolution than about R200 with grating (as stated in recent thread in spectroscopy section).

That lead me to finally understand coma and focus issues (which are consequence of grating equation and the fact that parts of beam are not perpendicular to grating), and after knowing all of that, I managed to "tweak" parameters to get much better resolution of spectrum. "Splitting" spectra by different focus points and then combining them should improve things further.

Here is example of calc for my 8" F/8:

I outlined worst offender - field curvature of the grating. By using multiple focus points (like say 4-5, and doing parts of spectrum separately and then joining them at the end), next problem will be coma. If I change calc so it does not include focus issues, here is resolution that I'm getting:

We can do a bit more tweaking to further improve things - add more dispersion to bring down impact of seeing (at expense of SNR, but that can be sorted with longer integration time / stacking / binning) and controlling coma with aperture mask:

Now ~R500 is quite decent for simple device like SA200.

28 minutes ago, andrew s said:

@vlaiv you can mitigate the spectral curvature by tilting the sensor with respect to the optic axis but then it makes the rest of the field defocused.

Also you need to keep the first order on the image to allow calibration of star without obvious sharp lines. This limits the grating chip distance you can have although vignetting  will also be an issue if you go too far.

Good luck with the project.

Regards Andrew

I thought about that - same thing prism does when used in "grism" configuration. Focusing on different parts of spectrum is a bit more involved, but should provide even better result if one chooses many focus points, and it can be automated to some extend with use of motor focuser as positions / shifts can be both calculated and observed/recorded for future use.

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@vlaiv practically focusing on the spectrum is difficult at the best of times. You could step through with a very accurate automated focuser.

I am not sure how you would identify the good bits and stich the spectrum together.

It might be practically simpler to use a grism or go fof a parallel beam arrangement.

Do you have a specific project in mind or just enjoying seeing what can be done?

Regards Andrew

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24 minutes ago, andrew s said:

@vlaiv practically focusing on the spectrum is difficult at the best of times. You could step through with a very accurate automated focuser.

I am not sure how you would identify the good bits and stich the spectrum together.

It might be practically simpler to use a grism or go fof a parallel beam arrangement.

Do you have a specific project in mind or just enjoying seeing what can be done?

Regards Andrew

No specific project in mind. Actually there is - more of a challenge then a project. Most of things to date were just theoretical, and recent discussion fueled my interest in actually going out and capturing some spectra. I've not used my SA200 much so far. One failed capture of spectrum (at the time I had no idea how to use it properly) - very poorly focused, I'll attach profile of capture without any processing - just to show that almost no features are visible. Did observe spectra of stars on couple of occasions.

I want to try to do star classification for purpose of determining approximate distance to stars (photometry and stellar class), but for the time being will settle just at practicing and capturing some decent spectra. Given the time it takes to setup everything, I want to make the most out of the session, instead of just capturing single spectrum (and reference for calibration) - that means a list of techniques to try out, and list of stars. Next will obviously be to see what sort of resolution can I realistically reach, by using different approaches - might even have a go with different scope - F/10 achromat stopped down a bit - it will have less light grasp, and focusing will be even more tricky due to different focus positions across the spectrum, but multiple focus positions should take care of that as well. It does offer very good theoretical resolution - over R600 (if we exclude effects of field curvature by means of stepped focusing).

All of this is really planning stage for some time under stars (which have been scarce lately, and not only due to poor weather, most of the time I can't be bothered to setup everything for some reason, so hopefully this fun activity will spark interest again).

Here is "failed" spectrum, I don't even remember gear I used to capture it, but I do know it was color camera. I did max stack of channels to produce mono image, but transitions between colors can be clearly seen in outline:

Can't really say I'm seeing any features in it

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Looks like you focused on the zero order star image....not the spectrum.

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1 hour ago, Merlin66 said:

Looks like you focused on the zero order star image....not the spectrum.

I believe it indeed was the case. I took that quite a long time ago, and realized that one should focus on spectrum some time after that (if I recall correctly), so that is a good chance I was not aware when I took it.

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